when i lived in iowa there was a place owned by a person displaced by hurricane katrina for a while and they had the best red beans and rice. it did not survive.
the restaurant business is unforgiving. my wife's uncle, now deceased, spent his entire life in it. the margins on everything are so small and the workers are generally unreliable.
there's a place i like in beverly hills that has moved twice since covid and i'm very worried about it. it's where my best friend and i always eat when i visit her.
the owner gives us free stuff to sample. i tell her, "stop doing this, this is a bad idea."
i didn't. i definitely ate at every taqueria within a 5 minute walk of campus. that looks like a 15 minute walk from campus.
that brought up another memory, when i was first looking for an apartment in berkeley, i was down there, and while i was touring an apartment a dog, apparently owned by nobody, came in and took an enormous piss on the otherwise nice hardwood floor.
in my first year in berkeley, two guys working together tried to ask me directions while the other tried to steal my backpack. of course i was trying hard to help so i reached for my backpack to get my map out and caught the f*.
one of my friends in grad school was beat up rather badly in front of a laundromat in south berkeley for the sum of $12. i've never dealt with that kind of criminality. most of what i've seen is understandable.
a lot of the mathematical pantheon is dodgy. rudin's real analysis. too much topology, measure theory jammed in at the end awkwardly. the sequences and series stuff is OK but generally it is a mess.
rudin's functional analysis. people only read that because they think it should be good because rudin's real analysis was said to be good. it's mediocre.
i've been known to wave red flags in front of bulls, if that is the instinct, i completely identify with it. i spend half of my day doing that. i just wonder if there's more to it than that.
have you considered a career in the legal industry.
there are a lot of shitty books in the 'intro to proof' category. a bunch of schools began teaching these classes as a kind of bridge between methods-driven calculation and argument-driven proof around the time when i was an undergraduate.
and tons of books came out for that purpose that were trash.
you see people under the influence of these books on math.SE. they want you to state things with $\forall$ and $\exists$ and put half of what you're saying in symbolic language.
i'm not against symbolic methods but you really have to use them if that's what you're doing. you can't use upside down and backwards letters as an excuse for not thinking.
not a fan of jobs, but he said something along the lines of there are only a few ways to get things right and an infinite number of ways of screwing up
note for example that you can have f^n(0) = 0 for all n without the function being the zero function. there are presumably examples on stackexchange.
for 'nice' functions you sometimes do get more expected results.
this does pop up in a lot of calculus books, where they sometimes prove a theorem about functions being represented by their taylor series without fully going into why that's even something you'd need to proove.
it's just there.
there's also an issue of the sense of the convergence. you wouldn't expect T_n(x) to converge to f(x) monotonically throughout the domain of its definition. there's going to be some bouncing around and that it will be better near where you're making the approximation than further away, but i don't know why you could expect T_n+1 at any point to be better than T_n.
a good starting point might be the remainder theorem for taylor series that calculus books include for nice enough functions. and its proof.
@user863565 that does not really illustrate what you mean. the taylor series are an approximation around a specific point in a particular way. if they exist they must be better approximations for larger $n$.
almost none of the stuff you see in a calculus book is optimal but it does often give indications of what will and won't happen in generality.
if i'm speaking gibberish someone please stomp on me. a fun exercise is to prove that for any sequence of real numbers a_n whatsoever, there is a smooth function f with f^n(0) = a_n. and to note that this fact violates a lot of the common assumptions used in calculus books to prove that functions are representable by their taylor series, which usually assume boundedness on the growth of a_n.
you can use linear combinations of appropriately scaled bump functions to solve the exercise i proposed above. i'm surprised that it isn't in more analysis books.
i sort of get it. an injection is a bijection into something.
I need some help in commutative algebra questions. Can anyone join me to discuss some problems in commutative algebra? We can discuss here in stack or in commutative algebra group (here)[t.me/algebracommutative]
To add to the other answers, one often does not need to use linear algebra to solve simple puzzles like this one. For this puzzle it suffices to observe that incrementing one face and decrementing another results in +1 to one vertex and −1 to an adjacent vertex, and clearly any such pair is possi...
^ Can anyone solve the dodecahedron case? In my answer I fully solve for the tetrahedron and octahedron, and in my comment I give a hint for the icosahedron. But the dodecahedron case seems much harder than the rest.
The dodecahedron case is not asked for in the question, but it piqued my curiosity.
uh, it's comparative statics in economics, so things are used pretty loosely mathematically speaking, but I like to read up on the rigorous background for stuff
stewart's calculus book isn't bad with differentials. not a lot of the general formalism in there, they're just linear functions whose variables are written funny.
perfectly rigorous although maybe not very enlightening.
i was just about to answer a functional analysis question and the poster deleted it. i guess that's better than deleting after i answered the question.
they must have figured it out. with a good question i recommend just answering yourself if you figure it out, instead of deletion.
the question was whether any normal linear functional on a von neumann algebra was a finite linear combination of normal states. the answer is yes and you need at most four of them.
when i moved across the country the postal service sent most of my books, including ones i never use about topology, but lost both volumes of kadison and ringrose and the first two volumes of takesaki. it's like the universe was telling me to quit math.
Let $F$ is a field and $F[x]$ is a polynomial ring with one variable. If $F[x]/I$ is a local ring such that $\dim_F(M/M^2)=1$ where $M$ is a maximal ideal of $F[x]/I$ (here, we view $M/M^2$ as a finite dimensional vector space over $F$) then $I = (x)^n$ for some $n\geq 1$.
I've already show tha...
Given a non-constant morphism $\phi\colon E_1\to E_2$ between projective (irreducible) curves $E_1$ and $E_2$, we can define the pull-back $\phi^*\colon K(E_2)\to K(E_1)$. The degree of $\phi$ is the degree of the field extension $K(E_1)/\phi^* K(E_2)$. So far so good, but now my book is claiming that the degree of $\phi$ is given by $\overline K(E_1)/\phi^*\overline K(E_2)$ (where clearly they extended the definition of $\phi^*$). Are those degrees always the same?
Otherwise I wouldn't know why my book is switching between them
what are the generators of the zeroth reduced homology for a space with $$\alpha$$ path components? is it just , for a fixed $0$-simplex $x_0$ in some fixed path component $C_0$, $x_{\alpha} - x_0$ for varying $\alpha$?
(for varying $\alpha \neq 0$)
(where $x_{\alpha} \in C_{\alpha}$ and $C_{\alpha}$ are the path components)
it feels like it should be, no two of these are homologous and all of these are in the kernel of $\epsilon : C_0(X) \rightarrow \mathbb{Z}$
one time about 25 years ago i was up early and dorking around on the internet and a meteor went over my neighborhood and made a terrifying boom. they move really fast. i didn't know what was happening.
i'll sit here with my ginger tea and not experience that.
i've never seen anything move that fast. my dad didn't believe me, then he confirmed it with some local authorities because he worked for a newspaper and they got like 50 calls about it.
there's a great piece in the latest new yorker about UFOs. that brought that incident back in mind.
oh, it's a fun result. or at least i think it is. every sequence of real numbers a_n is the sequence of taylor coefficients of a smooth function. this is to be compared to the results used in books (maxima taken over nth derivatives etc) to prove that various functions are indeed represented by their power series.
